The Exponential Versus the Complex Power e z Function Revisited

Luis M. Sánchez-Ruiz (), Matilde Legua, Santiago Moll-López, José A. Moraño-Fernández and María-Dolores Roselló
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Luis M. Sánchez-Ruiz: Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
Matilde Legua: Departmento de Matemática Aplicada, Universidad de Zaragoza, 50018 Zaragoza, Spain
Santiago Moll-López: Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
José A. Moraño-Fernández: Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
María-Dolores Roselló: Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2025, vol. 13, issue 8, 1-17

Abstract: The complex exponential function exp is a well-known entire function. In this paper, we recall its relation with the definition of the complex power of a complex number, which emanates that the complex power e z may coincide with it at some complex values. Still, on most occasions, the power represents a much broader spectrum of complex values. We also outsight how the software M a t h e m a t i c a may become a valuable tool for evaluating and visualizing complex power functions, in some cases by introducing some specific commands that have not been implemented in the software.

Keywords: complex variable; complex exponential; complex logarithm; complex power of a complex number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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